the n-dimensional volume of .
:In general, this can be defined given any measure on U, for instance by integration (e.g. Lebesgue integration) of .

* A real fuzzy set is said to be convex (in the fuzzy sense, not to be confused with a crisp convex set), iff
::.
: Without loss of generality, we may take x <= y, which gives the equivalent formulation
::.
: This definition can be extended to one for a general topological space U: we say the fuzzy set is convex when, for any subset Z of U, the condition
::
: holds, where denotes the boundary of Z and denotes the image of a set X (here ) under a function f (here ).